Proof of a conjecture of V. Nikiforov

Using analytical tools, we prove that for any simple graph G on n vertices and its complement [`(G)]\bar G the inequality $\mu \left( G \right) + \mu \left( {\bar G} \right) \leqslant \tfrac{4} {3}n - 1$\mu \left( G \right) + \mu \left( {\bar G} \right) \leqslant \tfrac{4} {3}n - 1 holds, where μ(G) and m( [`(G)] )\mu \left( {\bar G} \right) denote the greatest eigenvalue of adjacency matrix of the graphs G and [`(G)]\bar G respectively.     

Polymorphic evolution sequence and evolutionary branching

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence (TSS), is called polymorphic evolution sequence (PES). Then we introduce a scaling of the size of mutations and we study the PES in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. This phenomenon corresponds to the situation where the population, initially essentially single modal, is driven by the selective forces to divide into two separate subpopulations. To this end we finely analyze the asymptotic behavior of three-dimensional competitive Lotka?CVolterra systems.     

Integration by parts formula and applications to equations with jumps

We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes arising as the solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bichteler et?al. (Stochastics Monographs, vol 2. Gordon & Breach, New York, 1987) and Bismut (Z Wahrsch Verw Gebiete 63(2):147?C235, 1983) fails.     

Domino portrait generation: a fast and scalable approach

A domino portrait is an approximation of an image using a given number of sets of dominoes. This problem was first formulated in 1981 by Ken Knowlton in a patent application, which was finally granted in 1983. Domino portraits have been generated most often using integer linear programming techniques that provide optimal solutions, but these can be slow and do not scale well to larger portraits. In this paper we propose a new approach that overcomes these limitations and provides high quality portraits. Our approach combines techniques from operations research, artificial intelligence, and computer vision. Starting from a randomly generated template of blank domino shapes, a subsequent optimal placement of dominoes can be achieved in constant time when the problem is viewed as a minimum cost flow. The domino portraits one obtains are good, but not as visually attractive as optimal ones. Combining techniques from computer vision and large neighborhood search we can quickly improve the portraits. Empirically, we show that we obtain many orders of magnitude reduction in search time.     

Multiple critical points for a class of nonlinear functionals

In this paper, we prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. We apply our result to the nonlinear Schr?dinger–Maxwell system in ${\mathbb{R}^3}$ and to the nonlinear elliptic Kirchhoff equation in ${\mathbb{R}^N}$ assuming on the local nonlinearity the general hypotheses introduced by Berestycki and Lions.     

Differential calculus for linear operators represented by finite signed measures and applications

We introduce a differential calculus for linear operators represented by a family of finite signed measures. Such a calculus is based on the notions of g-derived operators and processes and g-integrating measures, g?being a right-continuous nondecreasing function. Depending on the choice of?g, this differential calculus works for non-smooth functions and under weak integrability conditions. For linear operators represented by stochastic processes, we provide a characterization criterion of g-differentiability in terms of characteristic functions of the random variables involved. Various illustrative examples are considered. As an application, we obtain an efficient algorithm to compute the Riemann zeta function ??(z) with a geometric rate of convergence which improves exponentially as ?(z) increases.     

Optimization of Streptomyces bacteriophage ��C31 integrase system to prevent post integrative gene silencing in pulmonary type II cells

φC31 integrase has emerged as a potent tool for achieving long-term gene expression in different tissues. The present study aimed at optimizing elements of φC31 integrase system for alveolar type II cells. Luciferase and β-galactosidase activities were measured at different time points post transfection. 5-Aza-2''deoxycytidine (AZA) and trichostatin A (TSA) were used to inhibit DNA methyltransferase and histone deacetylase complex (HDAC) respectively. In A549 cells, expression of the integrase using a CMV promoter resulted in highest integrase activity, whereas in MLE12 cells, both CAG and CMV promoter were equally effective. Effect of polyA site was observed only in A549 cells, where replacement of SV40 polyA by bovine growth hormone (BGH) polyA site resulted in an enhancement of integrase activity. Addition of a C-terminal SV40 nuclear localization signal (NLS) did not result in any significant increase in integrase activity. Long-term expression studies with AZA and TSA, provided evidence for post-integrative gene silencing. In MLE12 cells, both DNA methylases and HDACs played a significant role in silencing, whereas in A549 cells, it could be attributed majorly to HDAC activity. Donor plasmids comprising cellular promoters ubiquitin B (UBB), ubiquitin C (UCC) and elongation factor 1α (EF1α) in an improved backbone prevented post-integrative gene silencing. In contrast to A549 and MLE12 cells, no silencing could be observed in human bronchial epithelial cells, BEAS-2B. Donor plasmid coding for murine erythropoietin under the EF1α promoter when combined with φC31 integrase resulted in higher long-term erythropoietin expression and subsequently higher hematocrit levels in mice after intravenous delivery to the lungs. These results provide evidence for cell specific post integrative gene silencing with φC31 integrase and demonstrate the pivotal role of donor plasmid in long-term expression attained with this system.     

Permeability of Pore Networks Under Compaction

The characteristic pore length fixes the scale of permeability of a porous medium. For pore networks undergoing strong random compaction, this length becomes singular at transition porosities, revealing a change in the microstructure of the porespace controlling the transport. Nodal balances and lattice Boltzmann simulations of flow in pore networks under compaction show that the scaling between permeability and porosity changes near the transition porosities. Simulation results are compared with experimental permeability data from transparent two-dimensional micromodels of networks decorated with the same pore size distribution. Permeability?Cporosity data of media undergoing smooth compaction is well described by a single power law. Under strong compaction, however, the scaling between permeability and porosity is possible by traits only, the scaling exponent changes notably at given transition porosities. These behaviors are common to a wealth of permeability?Cporosity data thus far unexplained.